Transcript TEKTON 2.3 - Massachusetts Institute of Technology

Discussion of Tekton,
GeoFEM & Adina
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Differences in development path
Differences in cost/support available
Differences in size and capabilities
Issues for solving large problems:
– Direct solution vs iterative solution
– Serial vs parallel
• Shared vs distributed memory
• Disclaimer: informed opinion of non-expert
TEKTON 2.3
(aka Tecton)
TEKTON is a finite element computer code that is tailored
specifically to solve tectonic problems for geologists and
geophysicists. The FORTRAN source code is available at
website http://www.lpl.arizona.edu/tekton/, along with advice
from veteran users.
TEKTON has been developed over many years by [Jay
Melosh and] numerous people (the first of whom was Arthur
Raefsky). In addition to the old, very stable, program
TECTON 1.51, you will also find TEKTON 2.3. This is a much
more advanced version that employs sparse matrix storage
methods and hence can solve 3-D problems quite efficiently.
If you use this version, please regard it as a beta-test version.
I intend to upgrade TEKTON 2.3 very shortly . . . .
Last Updated: June 4, 1999
TEKTON 2.3
• Linear shape functions, brick elements
• Direct solution of Kd = f
• High accuracy
• sparse matrix
• Memory ~ n5/3 (n = number of nodes)
• Time to factor K ~ n5/3 ; to solve ~ n2
• N ~ nedge3; M ~ nedge5; t ~ nedge6
TEKTON 2.1 – Charles Williams
• Iterative solution of Kd = f
• Accuracy?
• Rate of convergence?
• Memory ~ n (n = number of nodes)
• Time to solve ~ n4/3 ~ nedge4
• Could have parallel implementation
– Distributed memory
GeoFEM
“Solid” Earth component of Earth
Simulator Project
http://geofem.tokyo.rist.or.jp/
4th GeoFEM Seminar
The University of Tokyo, Japan
July 18, 2002
>> DETAIL (Japanese)
>> DETAIL (PDF FILE 157KB)
3D Linear-Elastic Problem with 800M DOF on 128
nodes of the Hitachi SR8000 at the University of
Tokyo by 335 GFLOPS performance.
(December 10, 2001)
Research Organization for Information Science & Technology (RIST)
2-2-54, Nakameguro, Meguro-ku Tokyo, 153-0061, Japan
SSS2001
TEL: +81-3-3712-5321 FAX: +81-3-3712-5552
Workshop on Scalable
http://www.tokyo.rist.or.jp/
Solver Software
December 3-5, 2001
The University of Tokyo
>> DETAIL
Copyright(C)2001 Research Organization for Information Science & Technology (RIST) All Rights Reserved.
Top >> Software Download
GeoFEM Software Download
GeoFEM Version 4.0 Download
•GeoFEM Version 4.0 Basic Distribution Kit
•Collection of GeoFEM Version 4.0 Sample Data
•Thermal Fluid Analysis Subsystem for GeoFEM Version 4.0
Patch files for GeoFEM Version 4.0 Download
GPPView beta version
(GeoFEM Pre/Post Viewer Editor)
GeoFEM Manual Download
•English
•GeoFEM/Tiger Quick Start Ver.4.0 E "English Version"
•Japanese
•GeoFEM/Tiger Quick Start Ver.4.0 J "Japanese Version"
•"Static_Linear" Module User's Manual
•"Dynamic_Linear" Module User's Manual
•"Thermal" Module User's Manual
•"Plug-in" Manual
Availability of GeoFEM Software (Platform and
Parameters)
GeoFEM FAQ
GeoFEM Online Tutorial
GeoFEM node partitioning
Grid partitioning – Recursive
Coordinate Bisection, METIS
Example partitioning
Speed, memory comparison
TEKTON 2.3, 2.1 vs GeoFEM
• GeoFEM – elastic only (released now)
• Elastic - numerically challenging step
– Stress singularity at fault tip
• Correspondence principal – viscoelastic
• Do iterative techniques converge
quickly?
Try Benchmark 4?
Finite length strike-slip dislocation in rigid-walled box
Kluge: Use ½ box,
impose dislocation
as boundary
condition
GeoFEM Definition Language . . . .
begin structure_static_linear
!
format_version 4.0
title
example_used_for_caltech
analysis
elastic
!
begin solver
method
CG
precondition
SSOR
!
.. solver parameters ..
!
integer ; max. iteration, restart for GM
!
real
; conv. tol, diag. mul, non-diag
integer_parameter
20000
integer_parameter
1
real_parameter
1.0e-7
real_parameter
1.0
real_parameter
0.0
Run time vs n
• Tekton 2.3 direct solve: t ~ n2
• Tecton 2.1, GeoFEM iterative solve t ~ n4/3
Tecton 2.1 vs GeoFEM times
• Run times comparable
• Different preconditioners (IC(?) vs SSOR)
• Convergence criteria the same??
memory vs n
• Tekton 2.3 direct solve: M ~ n1.5
– Expected M ~ n1.67; non-K memory affects small n
• Tecton 2.1, GeoFEM iterative solve M ~ n
GeoFEM parallel performance
• Efficiency (e = t1/(N tN) and runtime
• tN vs number of processors, N
• 4 processor PC cluster
GeoFEM parallel performance
• Iteration inefficiency and memory/processor
vs number of processors
• Splitting the problem requires more iterations
Summary of elastic tests
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Iterative solution works!
Performance depends on preconditioner
Scalings with n as expected
Scalings with N look good
Need to extend comparisons to variable
grid and variable modulus
Adina
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http://www.adina.com/
MIT heritage (Bathe)
Commercial code
Many element types
Many rheological descriptions, dynamic, . . .
Shared memory
NOT distributed memory
Plan to use for benchmarks
Benchmark 7
Elastic solution for a circular strike-slip fault.
The purpose of this problem is to address how well our
codes handle curved faults. By symmetry, the radial
displacements should vanish.
The conceptual model is an elastic disk of radius 200 km,
with a circular left-lateral strike-slip fault forming an inner
plug rotating inside an outer annulus. Because of the
symmetry of the problem, only the first quadrant needs to be
calculated.
Analytic solution for infinite halfspace from Okada for
comparison
Okada solution
Grid forBenchmark
benchmark 7: 407km
thick quarter disk;
Grid
free at top, pinned at bottom
u_y pinned,
u_x, u_z free
u_x pinned, u_y, u_z free
Benchmark 7 – GAEA, r=100 km
GAEA BM7
(quadratic serendipity brick elements)
r = 100 km; average displacement (no split)
x dot u x cross dot/cross
u
X
Y
u_x
u_y
u_z
flt_perp flt_parallel
(m)
(m)
(m)
(m)
(m)
(cm)
(cm)
100000
0
0 -0.1332
0 0.0000 -13.32 0.00%
99690
7846 0.0119 -0.142 -0.002 0.0722 -14.25 -0.51%
98770 15640 0.0229 -0.1458 0.001 -0.0185 -14.76 0.13%
97240 23340 0.0339 -0.1419 1E-04 -0.0155 -14.59 0.11%
95110 30900 0.0448 -0.1381 2E-04 -0.0064 -14.52 0.04%
92390 38270 0.0558 -0.1346 -1E-04 0.0042 -14.57 -0.03%
89100 45400 0.0662
-0.13 2E-04 -0.0036 -14.59 0.02%
85260 52250 0.0762 -0.1243
0 0.0021 -14.58 -0.01%
80900 58780 0.0857 -0.1179
0 0.0030 -14.58 -0.02%
76040 64940 0.0946 -0.1108
0 -0.0020 -14.57 0.01%
70710 70710 0.1031 -0.1031
0 0.0000 -14.58 0.00%
64950 76040 0.1109 -0.0947
0 0.0020 -14.58 -0.01%
58780 80900 0.1179 -0.0857
0 -0.0030 -14.58 0.02%
52250 85260 0.1242 -0.0761
0 0.0012 -14.57 -0.01%
45400 89100
0.13 -0.0662 -2E-04 0.0036 -14.59 -0.02%
38270 92390 0.1346 -0.0558 1E-04 -0.0042 -14.57 0.03%
30900 95110 0.1381 -0.0448 -2E-04 0.0064 -14.52 -0.04%
23350 97240 0.1419 -0.034 -1E-04 0.0072 -14.59 -0.05%
15640 98770 0.1458 -0.0229 -0.001 0.0185 -14.76 -0.13%
7847 99690 0.142 -0.0119 0.002 -0.0720 -14.25 0.51%
0 100000 0.1332
0
0 0.0000 -13.32 0.00%
Okada (1/2 space):
-17.92
Benchmark 7 – GAEA, r=120 km
GAEA BM7
(quadratic serendipity brick elements)
r = 120 km; average displacement (no split) x dot u x cross dot/cross
u
X
Y
u_x
u_y
u_z
flt_perp flt_parallel
(m)
(m)
(m)
(m)
(m)
(cm)
(cm)
120000
0
0 0.0989
0 0.0000 11.87 0.00%
119600
9415 -0.0102 0.0992 0.0003 -0.2860 11.96 -2.39%
118500 18770 -0.0144 0.0978 -0.0003 0.1293 11.86 1.09%
116700 28010 -0.0227 0.0957 -0.0001 0.0315 11.80 0.27%
114100 37080 -0.0306 0.0944
0 0.0089 11.91 0.07%
110900 45920 -0.0378 0.0913
0 0.0005 11.86 0.00%
106900 54480 -0.0449 0.0883
0 0.0108 11.89 0.09%
102300 62700 -0.0517 0.0844
0 0.0030 11.88 0.03%
97080 70530 -0.0582 0.0801
0 -0.0006 11.88 -0.01%
91250 77930 -0.0642 0.0752
0 0.0021 11.87 0.02%
84850 84850
-0.07
0.07
0 0.0000 11.88 0.00%
77930 91250 -0.0752 0.0642
0 -0.0021 11.87 -0.02%
70530 97080 -0.0801 0.0582
0 0.0006 11.88 0.01%
62700 102300 -0.0844 0.0517
0 -0.0030 11.88 -0.03%
54480 106900 -0.0883 0.0449
0 -0.0108 11.89 -0.09%
45920 110900 -0.0913 0.0378
0 -0.0005 11.86 0.00%
37080 114100 -0.0944 0.0306
0 -0.0089 11.91 -0.07%
28010 116700 -0.0957 0.0227 0.0001 -0.0315 11.80 -0.27%
18770 118500 -0.0978 0.0144 0.0003 -0.1293 11.86 -1.09%
9416 119600 -0.0992 0.0102 -0.0003 0.2859 11.96 2.39%
0 120000 -0.0989
0
0 0.0000 11.87 0.00%
Okada 1/2 space:
10.12
Benchmark 7 – ABAQUS, r=120 km, linear elements
ABAQUS, linear elements, 10 km spacing
x
y
u_x
u_y
u_z
(km) (km) (km)
(km)
(km)
120.00
119.63
118.52
116.68
114.13
110.87
106.92
102.32
97.08
91.25
84.85
77.93
70.53
62.70
54.48
45.92
28.01
18.77
9.42
0.00
0.00
9.42
18.77
28.01
37.08
45.92
54.48
62.70
70.53
77.93
84.85
91.25
97.08
102.32
106.92
110.87
116.68
118.52
119.63
120.00
-4.67E-23
-3.11E-09
2.37E-08
3.33E-08
4.81E-08
5.56E-08
6.80E-08
7.61E-08
8.70E-08
9.49E-08
1.04E-07
1.12E-07
1.20E-07
1.26E-07
1.33E-07
1.40E-07
1.62E-07
1.77E-07
1.96E-07
2.11E-07
-2.11E-07
-1.96E-07
-1.77E-07
-1.62E-07
-1.49E-07
-1.40E-07
-1.33E-07
-1.26E-07
-1.20E-07
-1.12E-07
-1.04E-07
-9.49E-08
-8.70E-08
-7.61E-08
-6.80E-08
-5.56E-08
-3.33E-08
-2.37E-08
3.11E-09
-2.36E-23
-1.01E-07
-4.83E-08
-1.79E-08
-4.84E-09
-9.05E-10
3.39E-10
2.25E-10
2.37E-10
7.73E-12
3.17E-11
-1.21E-22
-3.17E-11
-7.73E-12
-2.37E-10
-2.25E-10
-3.39E-10
4.84E-09
1.79E-08
4.83E-08
1.01E-07
r
x*u
(km) flt perp
(cm)
120 0.0000
120 -2.2195
120 -0.5123
120 -0.6390
120 -0.0343
120 -0.2837
120 0.0037
120 -0.1295
120 0.0041
120 -0.0382
120 0.0000
120 0.0382
120 -0.0041
120 0.1295
120 -0.0037
120 0.2837
120 0.6390
120 0.5123
120 2.2195
120 0.0000
x X u */X
flt paralperp/paral
(cm)
-25.26 0.00%
-23.45 9.47%
-21.43 2.39%
-19.80 3.23%
-18.77 0.18%
-18.12 1.57%
-17.97 -0.02%
-17.69 0.73%
-17.75 -0.02%
-17.58 0.22%
-17.71 0.00%
-17.58 -0.22%
-17.75 0.02%
-17.69 -0.73%
-17.97 0.02%
-18.12 -1.57%
-19.80 -3.23%
-21.43 -2.39%
-23.45 -9.47%
-25.26 0.00%
Benchmark 7 – ABAQUS, r=120 km, quadratic elements
ABAQUS, quadratic elements, 10 km spacing, r=120 km
x
y
u_x
u_y
u_z
r
x*u
(km) (km) (km)
(km)
(km)
(km) flt perp
(cm)
120.00
0.00 -4.58E-23 -2.06E-07 -9.62E-08 120 0.0000
119.26
9.39 1.86E-09 -2.04E-07 -4.78E-08 120 -1.6957
118.52 18.77 2.44E-08 -1.81E-07 -1.91E-08 120 -0.4950
116.32 27.93 3.65E-08 -1.68E-07 -6.24E-09 120 -0.4646
114.13 37.08 4.83E-08 -1.56E-07 -1.89E-09 120 -0.2498
110.52 45.78 6.03E-08 -1.50E-07 -1.99E-10 120 -0.1794
106.92 54.48 6.97E-08 -1.39E-07 1.63E-11 120 -0.1018
102.00 62.51 8.18E-08 -1.35E-07 6.31E-11 120 -0.0708
97.08 70.53 8.97E-08 -1.24E-07 5.61E-11 120 -0.0415
90.97 77.69 1.02E-07 -1.19E-07 -3.75E-12 120 -0.0211
84.85 84.85 1.08E-07 -1.08E-07 -1.07E-23 120 0.0000
77.69 90.97 1.19E-07 -1.02E-07 3.75E-12 120 0.0211
70.53 97.08 1.24E-07 -8.97E-08 -5.61E-11 120 0.0415
62.51 102.00 1.35E-07 -8.18E-08 -6.31E-11 120 0.0708
54.48 106.92 1.39E-07 -6.97E-08 -1.63E-11 120 0.1018
45.78 110.52 1.50E-07 -6.03E-08 1.99E-10 120 0.1794
37.08 114.13 1.56E-07 -4.83E-08 1.89E-09 120 0.2498
27.93 116.32 1.68E-07 -3.65E-08 6.24E-09 120 0.4646
9.39 119.26 2.04E-07 -1.86E-09 4.78E-08 120 1.6957
0.00 120.00 2.06E-07 -2.31E-23 9.62E-08 120 0.0000
x X u */X
flt paralperp/paral
(cm)
-24.76 0.00%
-24.37 6.96%
-21.86 2.26%
-20.62 2.25%
-19.54 1.28%
-19.29 0.93%
-18.62 0.55%
-18.84 0.38%
-18.37 0.23%
-18.72 0.11%
-18.32 0.00%
-18.72 -0.11%
-18.37 -0.23%
-18.84 -0.38%
-18.62 -0.55%
-19.29 -0.93%
-19.54 -1.28%
-20.62 -2.25%
-24.37 -6.96%
-24.76 0.00%
Benchmark 7 – ABAQUS, r=120 km, quadratic elements
ABAQUS quadratic elements, 5 km spacing, r = 120 km,
x
y
u_x
u_y
u_z
r
x*u
(km) (km) (km)
(km)
(km)
(km) flt perp
(cm)
120.00 0.00 -4.74E-23 -2.13E-07 -9.20E-08 120 0.0000
119.82 4.71 -5.43E-09 -2.11E-07 -6.79E-08 120 -1.6453
119.63 9.42 5.75E-09 -2.04E-07 -4.66E-08 120 -1.2290
119.08 14.09 1.31E-08 -1.96E-07 -3.05E-08 120 -1.2005
118.52 18.77 2.23E-08 -1.86E-07 -1.91E-08 120 -0.8456
117.60 23.39 2.96E-08 -1.78E-07 -1.15E-08 120 -0.6852
116.68 28.01 3.66E-08 -1.70E-07 -6.60E-09 120 -0.4832
115.41 32.55 4.29E-08 -1.64E-07 -3.53E-09 120 -0.3860
114.13 37.08 4.88E-08 -1.58E-07 -1.77E-09 120 -0.2878
112.50 41.50 5.47E-08 -1.54E-07 -7.36E-10 120 -0.2308
110.87 45.92 6.00E-08 -1.49E-07 -2.28E-10 120 -0.1781
108.89 50.20 6.58E-08 -1.46E-07 3.62E-11 120 -0.1439
106.92 54.48 7.09E-08 -1.41E-07 1.17E-10 120 -0.1136
104.62 58.59 7.65E-08 -1.38E-07 1.39E-10 120 -0.0914
102.32 62.70 8.13E-08 -1.34E-07 1.11E-10 120 -0.0720
99.70 66.62 8.68E-08 -1.31E-07 8.33E-11 120 -0.0564
97.08 70.53 9.14E-08 -1.26E-07 5.07E-11 120 -0.0427
94.17 74.23 9.66E-08 -1.23E-07 3.02E-11 120 -0.0308
91.25 77.93 1.01E-07 -1.18E-07 1.40E-11 120 -0.0200
88.05 81.39 1.06E-07 -1.15E-07 5.83E-12 120 -0.0098
84.85 84.85 1.10E-07 -1.10E-07 -6.00E-22 120 0.0000
x X u */X
flt paral
(cm)
-25.61 0.00%
-25.30 6.50%
-24.41 5.03%
-23.49 5.11%
-22.42 3.77%
-21.61 3.17%
-20.81 2.32%
-20.32 1.90%
-19.82 1.45%
-19.56 1.18%
-19.25 0.93%
-19.15 0.75%
-18.95 0.60%
-18.92 0.48%
-18.79 0.38%
-18.81 0.30%
-18.71 0.23%
-18.75 0.16%
-18.67 0.11%
-18.73 0.05%
-18.66 0.00%